Defining parameters
Level: | \( N \) | \(=\) | \( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2550.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 41 \) | ||
Sturm bound: | \(1080\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2550))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 564 | 52 | 512 |
Cusp forms | 517 | 52 | 465 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | \(17\) | Fricke | Dim. |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(3\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(2\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(4\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(4\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(2\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(3\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(3\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(2\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(4\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(4\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(5\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(1\) |
Plus space | \(+\) | \(21\) | |||
Minus space | \(-\) | \(31\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2550))\) into newform subspaces
Label | Dim. | \(A\) | Field | CM | Traces | A-L signs | $q$-expansion | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(a_2\) | \(a_3\) | \(a_5\) | \(a_7\) | 2 | 3 | 5 | 17 | |||||||
2550.2.a.a | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(-1\) | \(0\) | \(-3\) | \(+\) | \(+\) | \(-\) | \(+\) | \(q-q^{2}-q^{3}+q^{4}+q^{6}-3q^{7}-q^{8}+\cdots\) | |
2550.2.a.b | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(-1\) | \(0\) | \(-2\) | \(+\) | \(+\) | \(+\) | \(-\) | \(q-q^{2}-q^{3}+q^{4}+q^{6}-2q^{7}-q^{8}+\cdots\) | |
2550.2.a.c | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(-1\) | \(0\) | \(0\) | \(+\) | \(+\) | \(+\) | \(+\) | \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\) | |
2550.2.a.d | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(-1\) | \(0\) | \(0\) | \(+\) | \(+\) | \(+\) | \(+\) | \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\) | |
2550.2.a.e | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(-1\) | \(0\) | \(0\) | \(+\) | \(+\) | \(-\) | \(+\) | \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\) | |
2550.2.a.f | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(-1\) | \(0\) | \(3\) | \(+\) | \(+\) | \(+\) | \(+\) | \(q-q^{2}-q^{3}+q^{4}+q^{6}+3q^{7}-q^{8}+\cdots\) | |
2550.2.a.g | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(-1\) | \(0\) | \(5\) | \(+\) | \(+\) | \(-\) | \(-\) | \(q-q^{2}-q^{3}+q^{4}+q^{6}+5q^{7}-q^{8}+\cdots\) | |
2550.2.a.h | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(-3\) | \(+\) | \(-\) | \(+\) | \(+\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\) | |
2550.2.a.i | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(-2\) | \(+\) | \(-\) | \(+\) | \(-\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\) | |
2550.2.a.j | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(-1\) | \(+\) | \(-\) | \(-\) | \(+\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\) | |
2550.2.a.k | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(-1\) | \(+\) | \(-\) | \(-\) | \(-\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\) | |
2550.2.a.l | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(0\) | \(+\) | \(-\) | \(+\) | \(+\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\) | |
2550.2.a.m | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(1\) | \(+\) | \(-\) | \(+\) | \(-\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\) | |
2550.2.a.n | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(4\) | \(+\) | \(-\) | \(+\) | \(+\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\) | |
2550.2.a.o | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(4\) | \(+\) | \(-\) | \(-\) | \(-\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\) | |
2550.2.a.p | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(4\) | \(+\) | \(-\) | \(-\) | \(-\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\) | |
2550.2.a.q | \(1\) | \(20.362\) | \(\Q\) | None | \(-1\) | \(1\) | \(0\) | \(4\) | \(+\) | \(-\) | \(+\) | \(+\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}+4q^{7}-q^{8}+\cdots\) | |
2550.2.a.r | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(-1\) | \(0\) | \(-4\) | \(-\) | \(+\) | \(+\) | \(+\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\) | |
2550.2.a.s | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(-1\) | \(0\) | \(-4\) | \(-\) | \(+\) | \(-\) | \(+\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\) | |
2550.2.a.t | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(-1\) | \(0\) | \(-4\) | \(-\) | \(+\) | \(-\) | \(-\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}-4q^{7}+q^{8}+\cdots\) | |
2550.2.a.u | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(-1\) | \(0\) | \(-2\) | \(-\) | \(+\) | \(+\) | \(-\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}-2q^{7}+q^{8}+\cdots\) | |
2550.2.a.v | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(-1\) | \(0\) | \(-1\) | \(-\) | \(+\) | \(-\) | \(+\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\) | |
2550.2.a.w | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(-1\) | \(0\) | \(1\) | \(-\) | \(+\) | \(+\) | \(-\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\) | |
2550.2.a.x | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(-1\) | \(0\) | \(1\) | \(-\) | \(+\) | \(+\) | \(+\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{7}+q^{8}+\cdots\) | |
2550.2.a.y | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(-1\) | \(0\) | \(2\) | \(-\) | \(+\) | \(+\) | \(+\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}+2q^{7}+q^{8}+\cdots\) | |
2550.2.a.z | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(-1\) | \(0\) | \(3\) | \(-\) | \(+\) | \(-\) | \(-\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}+3q^{7}+q^{8}+\cdots\) | |
2550.2.a.ba | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(1\) | \(0\) | \(-5\) | \(-\) | \(-\) | \(+\) | \(+\) | \(q+q^{2}+q^{3}+q^{4}+q^{6}-5q^{7}+q^{8}+\cdots\) | |
2550.2.a.bb | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(1\) | \(0\) | \(-3\) | \(-\) | \(-\) | \(-\) | \(-\) | \(q+q^{2}+q^{3}+q^{4}+q^{6}-3q^{7}+q^{8}+\cdots\) | |
2550.2.a.bc | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(1\) | \(0\) | \(-2\) | \(-\) | \(-\) | \(+\) | \(+\) | \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\) | |
2550.2.a.bd | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(1\) | \(0\) | \(0\) | \(-\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\) | |
2550.2.a.be | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(1\) | \(0\) | \(2\) | \(-\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\) | |
2550.2.a.bf | \(1\) | \(20.362\) | \(\Q\) | None | \(1\) | \(1\) | \(0\) | \(3\) | \(-\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+q^{3}+q^{4}+q^{6}+3q^{7}+q^{8}+\cdots\) | |
2550.2.a.bg | \(2\) | \(20.362\) | \(\Q(\sqrt{33}) \) | None | \(-2\) | \(-2\) | \(0\) | \(-1\) | \(+\) | \(+\) | \(+\) | \(-\) | \(q-q^{2}-q^{3}+q^{4}+q^{6}-\beta q^{7}-q^{8}+\cdots\) | |
2550.2.a.bh | \(2\) | \(20.362\) | \(\Q(\sqrt{5}) \) | None | \(-2\) | \(2\) | \(0\) | \(-2\) | \(+\) | \(-\) | \(-\) | \(+\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}+(-1-\beta )q^{7}+\cdots\) | |
2550.2.a.bi | \(2\) | \(20.362\) | \(\Q(\sqrt{6}) \) | None | \(-2\) | \(2\) | \(0\) | \(0\) | \(+\) | \(-\) | \(-\) | \(-\) | \(q-q^{2}+q^{3}+q^{4}-q^{6}+\beta q^{7}-q^{8}+\cdots\) | |
2550.2.a.bj | \(2\) | \(20.362\) | \(\Q(\sqrt{6}) \) | None | \(2\) | \(-2\) | \(0\) | \(0\) | \(-\) | \(+\) | \(-\) | \(+\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}+\beta q^{7}+q^{8}+\cdots\) | |
2550.2.a.bk | \(2\) | \(20.362\) | \(\Q(\sqrt{5}) \) | None | \(2\) | \(-2\) | \(0\) | \(2\) | \(-\) | \(+\) | \(-\) | \(-\) | \(q+q^{2}-q^{3}+q^{4}-q^{6}+(1+\beta )q^{7}+\cdots\) | |
2550.2.a.bl | \(2\) | \(20.362\) | \(\Q(\sqrt{6}) \) | None | \(2\) | \(2\) | \(0\) | \(0\) | \(-\) | \(-\) | \(+\) | \(-\) | \(q+q^{2}+q^{3}+q^{4}+q^{6}+\beta q^{7}+q^{8}+\cdots\) | |
2550.2.a.bm | \(2\) | \(20.362\) | \(\Q(\sqrt{33}) \) | None | \(2\) | \(2\) | \(0\) | \(1\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{3}+q^{4}+q^{6}+\beta q^{7}+q^{8}+\cdots\) | |
2550.2.a.bn | \(3\) | \(20.362\) | 3.3.568.1 | None | \(-3\) | \(-3\) | \(0\) | \(-6\) | \(+\) | \(+\) | \(-\) | \(-\) | \(q-q^{2}-q^{3}+q^{4}+q^{6}+(-2-\beta _{1}+\cdots)q^{7}+\cdots\) | |
2550.2.a.bo | \(3\) | \(20.362\) | 3.3.568.1 | None | \(3\) | \(3\) | \(0\) | \(6\) | \(-\) | \(-\) | \(-\) | \(+\) | \(q+q^{2}+q^{3}+q^{4}+q^{6}+(2+\beta _{1})q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2550))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2550)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(850))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1275))\)\(^{\oplus 2}\)